Is it possible to have a kidney stone stuck around my prostate on the way out but with ni pain? or even a tiny stone will cause pain?

Possible: It's possible that a stone of some sort could be stuck . Stones that form in the kidneys and travel through the ureters can get stuck as they enter the bladder. Stones in the bladder can get stuck on their way out. If they r small enough they may not cause pain. If its not bothersome then i wouldn't worry about it.

If the stone is not: Causing continued blockage of the ureter and kidney and is just in the bladder then you wouldn't have pain. If the kidney and ureter remain chronically obstructed the kidney will stop excreting urine and pressure in the system will drop and pain fade. Long term obstruction will degrade future kidney function the distinction is important.